Doubly Extended Lie Groups - Curvature, Holonomy and Parallel Spinors

Abstract

(This is a revised version of the paper) - In the present paper we study the geometry of doubly extended Lie groups with their natural biinvariant metric. We describe the curvature, the holonomy and the space of parallel spinors. This is completely done for all simply connected groups with biinvariantmetric of Lorentzian signature $(1,n-1)$, of signature $(2,n-2)$ and of signature $(p,q)$, where $p+q\leq 6$. Furthermore, some special series with higher signature are discussed.